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Recently a distribution free approach for testing parametric hypotheses basedon unitary transformations has been suggested in \cite{Khm13, Khm16, Khm17} andfurther studied in \cite{Ngu17} and \cite{Rob19}. In this note we show that thetransformation takes extremely simple form in distribution free testing oflinear regression. Then we extend it to general parametric regression withvector-valued covariates.

Distribution free testing for linear regression. Extension to general parametric regression